where \(L(-\infty )\)  is the initial condition in the infinite past, which requires the input from new physics (such as quantum gravity) to fully determine its value, in light of the Hawking-Penrose's singularity theorem [1]}. Therefore \(L(-\infty )\)  remains unknown to me due to my ignorance and obtuseness. On the other hand, one may try to take the integration from the other side, namely
\(L=\int ^{\infty }_{t}\frac{Ndt^{\prime }}{a(t^{\prime })}+L(+\infty ),\) 
